Question

A car starts from rest on a circular curve with a radius of 120 m and accelerates tangentially at 1.0 m/s2
.
Through what angle will the car have travelled when the magnitude of its total acceleration is 2.0 m/s2

Answer 1

total a = v^2/R inward + dv/dt tangent
but v = w R, w (omega) in radians/second of arc
so
a = v^2 / R inward + 1.0 tangentially
v = tangential acceleration * t = 1 t
|a| = sqrt ( t^4/R^2 t^2 + 1 ) = 2
so
t^2/R =3
t^2 = 3 * 120
t =19 seconds
w R = v
so
R d w/dt = dv/dt = 1 m/s^2
dw/dt = 1 / 120 radians/second^2
w = dw/dt *t = (1/120)(19) = 0.158 radians /s * 180/3.14) =9.1degrees/sec
theta = (1/2) (1/120)(19^2 ) = 1.5 radians = 86.2 degrees